The mathematics of non-linear metrics for nested networks

Abstract

Numerical analysis of data from international trade and ecological networks has shown that the non-linear fitness-complexity metric is the best candidate to rank nodes by importance in bipartite networks that exhibit a nested structure. Despite its relevance for real networks, the mathematical properties of the metric and its variants remain largely unexplored. Here, we perform an analytic and numeric study of the fitness-complexity metric and a new variant, called minimal extremal metric. We rigorously derive exact expressions for node scores for perfectly nested networks and show that these expressions explain the non-trivial convergence properties of the metrics. A comparison between the fitness-complexity metric and the minimal extremal metric on real data reveals that the latter can produce improved rankings if the input data are reliable.

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Cited by in corpus (12)

• Nestedness in complex networks: Observation, emergence, and implications
• Ranking in evolving complex networks
• Quantifying China's Regional Economic Complexity
• The Impact of Services on Economic Complexity: Service Sophistication as Route for Economic Growth
• Computational Socioeconomics
• Complexity, Centralization, and Fragility in Economic Networks
• Forecasting countries' gross domestic product from patent data
• The complex dynamics of products and its asymptotic properties
• Measuring nodes centrality when local and global measures overlap
• Complexity of products: the effect of data regularisation
• Equivalence between the Fitness-Complexity and the Sinkhorn-Knopp algorithms
• Cost Functions in Economic Complexity